The present invention relates to control systems for heating, ventilating and air conditioning (HVAC) systems, and in particular to calibrated sensing of air flow in such systems.
Heating, ventilating and air conditioning (HVAC) systems are designed and installed to maintain environmental conditions within buildings for the comfort of the occupants. A typical installation divides the building into zones and the HVAC system is adapted to maintain each zone within predefined environmental parameters (e.g., temperature, humidity, outdoor/recirculated air ratio, etc.). An air handling unit (A.U.) supplies conditioned air to ductwork that distributes the air to each of the zones. The air handling unit generally includes elements for introducing outdoor air into the system and for exhausting air from the system. Other elements heat, cool, filter and otherwise condition the air which circulates through air distribution ducts at a desired flow rate.
Air flow from the air handling unit to different regions of the zone is regulated by a separate variable air volume (VAV) terminal unit, also called a VAV box. The typical variable air volume terminal unit has a damper driven by an actuator to vary the flow of air from the air distribution duct into the associated zone region. Variable air volume terminal units serving zones on exterior walls typically have a heating element to increase the temperature of the air that flows in to the associated room. The these components are operated by a controller in response to signals from devices that sense air temperature and flow rate.
The air flow rate commonly is measured using a pitot tube which produces a differential pressure signal that is related in a non-linear manner to the flow rate. The VAV box controller calculates the air flow rate from the differential pressure signal. The determination of the flow rate often is simplified by assuming that air is incompressible, thereby allowing equation (1) to be derived from the well known Bernoulli equation;
{dot over (xcfx89)}=Cxc2x7Axc2x7{square root over (xcex94P)}xe2x80x83xe2x80x83(1)
where {dot over (xcfx89)} is the flow rate, C is a coefficient related primarily to the fluid density, A is the cross-sectional area where the flow rate is measured, and xcex94P is the differential pressure measured across the orifice or the velocity pressure measured by a pitot tube.
Because the value of the pressure differential xcex94P is very small and difficult to measure at very low flow rates, the pressure differential often is amplified by sensing the static pressure in a low pressure region immediately behind the orifice. In this case the flow rate is commonly calculated by the expression:                               ω          .                =                  C          ·          A          ·                                                    Δ                ⁢                                  xe2x80x83                                ⁢                P                            k                                                          (        2        )            
where k is a gain factor equal to the ratio of the measured differential pressure to the actual differential pressure between the flow streams immediately before and after the orifice. In current air flow balancing practices, the value of k is assumed to be constant throughout the operating range. The value of k is determined for each VAV terminal unit in an HVAC system based on empirical measurement of the actual flow rate with a calibrated sensor. The derivation of k typically is performed at the minimum flow rate for the VAV terminal unit and then inputted into the unit""s controller as a value to use in solving equation (2). However, because the relationship of the pressure differential to air flow does not exactly match equation 2, this process does not calibrate the VAV terminal unit at other flow rates.
An apparatus for measuring an unknown flow rate of a fluid can be calibrated at two flow rates, for example the minimum and maximum flow rates expected for the fluid. This dual calibration provides greater accuracy subsequently when measuring an unknown flow rate.
The calibration is performed by causing the fluid to flow at a first rate past a flow sensor, such as a pitot tube, of the apparatus. At that time, a first pressure reading across the flow sensor is obtained. In the preferred embodiment the pressure sensor reading indicates a differential pressure. A flow rate meter is used to measure the flow of fluid, thereby producing a relatively accurate first flow rate measurement.
Then the fluid is caused to flow past the flow sensor at a second rate while a second pressure reading across the flow sensor is obtained. At this time, the flow rate meter is used to measure the flow of fluid, thereby producing a relatively accurate second flow rate measurement.
The first pressure reading, the second pressure reading, the first flow rate measurement and the second flow rate measurement are used to calculate a first gain factor coefficient ao and a second gain factor coefficient a1.
Thereafter, the first and second flow rate measurements are employed to measure an unknown flow rate of the fluid based on a reading P from the pressure sensor. For example the unknown flow rate {dot over (xcfx89)} using the expression:       ω    .    =      Z    ·                                        xe2x80x83                    ⁢          P                                      a            0                    +                                    a              1                        *            P                              
where Z has a predefined value. For example, depending upon the derivation of the first and second gain factor coefficients a0 and a1, Z may have a value of one or be equal to the product of a coefficient of fluid density and the cross-sectional area of a conduit through which the fluid is flowing.
In the preferred versions of the calibration technique, the second gain factor coefficient a1 is calculated according to the expression:       a    1    =                    Z        2                    (                              P            2                    -                      P            1                          )              ·          (                                    P            2                                              ω              .                        2            2                          -                              P            1                                              ω              .                        2            2                              )      
where P1 is the first pressure reading, P2 is the second pressure reading, {dot over (xcfx89)}1 is the first flow rate measurement, and {dot over (xcfx89)} 2 is the second flow rate measurement. The first gain factor coefficient a0 is calculated according to the expression:       a    0    =            P      1        ·          [                                    (                          Z                                                ω                  .                                1                                      )                    2                -                  a          1                    ]      